• 8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.
  

  Geometry

  8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.

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• 8.G.A.1.B — Angles are taken to angles of the same measure.
  

  Geometry

  8.G.A.1.B — Angles are taken to angles of the same measure.

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• 8.G.A.1.C — Parallel lines are taken to parallel lines.
  

  Geometry

  8.G.A.1.C — Parallel lines are taken to parallel lines.

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• 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  

  Geometry

  8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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• 4.MD.C.6
  

  Measurement and Data

  4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

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Figure 1 is shown in the coordinate plane below. 

Which figure(s) would Figure 1 map to if it were 

• translated?
• reflected?
• rotated?

Below is a picture of two rectangles with the same length and width:

1. Show that the rectangles are congruent by finding a translation followed by a rotation that maps one of the rectangles to the other
2. Explain why the congruence of the two rectangles cannot be shown by translating Rectangle 1 to Rectangle 2.

Figures $${J, K, L, M, N,}$$ and $$P$$ are shown on the coordinate plane.

Part A:

Which figure can be transformed into Figure P by a translation 2 units to the right followed by a reflection across the $$x-$$axis?

a.     Figure J

b.     Figure K

c.     Figure L

d.    Figure M

Part B: Which figure can be transformed into Figure L by a 90-degree rotation clockwise about the origin followed by a translation 2 units down? 

a.     Figure J

b.     Figure M

c.     Figure N

d.     Figure P

Triangle $${{ABC}}$$ is rotated $${90^{\circ}}$$ clockwise around the origin.

Which of the statements below are true? Select all that apply.

a.     Point $${{B'}}$$ will be located at $${(1, 4)}$$.

b.     Point $${{B'}}$$ will be located at $${(4,1)}$$.

c.     $$\overline{{{B'}}C'}$$ will be a vertical line.

d.     $$\overline{{{B'}}C'}$$ will be parallel to $${\overline{BC}}$$.

e.     The area of $$A'{{B'}}C'$$ will be greater than the area of $${{ABC}}$$, but the perimeters will be the same.

f.     Both the areas and perimeters of the original and the rotated figures will be the same.

Describe how you can use transformations to show that the two figures below are congruent.